Constructivist Math in Common Core Standards?

Here is a video illustrating constructivist math techniques in an elementary classroom:

According to truthinamericaneducation.com, Common Core standards promote "collaborative" learning in the classroom as they place emphasis on Standards for Mathematical Practice which supports a constructivist approach.  You can read the research of the standards at the link.  The teacher's role is relegated to that of a facilitator.  I asked a math teacher to review this video.  His comments:

I could probably argue both sides of this. The students in the video seem to have this system well practiced. This might not be a bad practice with some aspects of it changed or removed and that it is not used every time a paper is checked. Occasionally might not be too bad but on a regular basis I would be concerned about the amount of instructional time that would be lost.

 What is taking place calls for peer teaching.  I don't send my kid to school for her to have to teach other kids (although that too often happens).  I send her to school to be taught. Unfortunately, the school doesn't see it that way.

 Having to reach consensus on whether a math problem is correct?  What?  That is where I lost it.  As long as we reach agreement all is okay?  Answers to math problems are either right or they are wrong.  Determining that an answer is correct is not a consensus activity---it is a "prove it" activity. I guess if two kids reach consensus that 2 + 3 = 6 then it must be so because they are in agreement.

 While some of the kids were having some good math discussion, what are we teaching kids when we have them use consensus to determine right or wrong.  A larger concern is that kids will learn to use consensus to determine what is morally and ethically right or wrong----no matter what the issue as long as they are in agreement.

Punishment for lack of consensus?  Really now?  What is the larger lesson students might learn from this.  Is it more important to agree with each other than for one to stand by empirical evidence even when not able to convince his partner?  Do we not promote standing up for what is right?  Will students reach consensus simply to avoid punishment? 

Here's another video (entitled "A primer for parents") by Bruce Deitrick Price questioning constructivist theory and practice. It is a good study for non-educators and parents to understand why collaborative learning might not be in your child's best educational interest but a good idea for CCSS adherence:

It might be a good idea to write down some of the statements in this second video and take it to your child's teacher if he/she is supportive of using collaborative learning projects instead of encouraging independent study. Price writes in the description of the video:

Constructivism is the main gizmo inside of Reform Math. 

Are consortia set standards supporting constructivist techniques in the best interest of your child?